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Littlewood conjecture: for any two real numbers ,, ‖ ‖ ‖ ‖ =, where ‖ ‖ is the distance from to the nearest integer. Mahler's 3/2 problem that no real number x {\displaystyle x} has the property that the fractional parts of x ( 3 / 2 ) n {\displaystyle x(3/2)^{n}} are less than 1 / 2 {\displaystyle 1/2} for all positive integers n ...
Projection of the Kardashev scale to 2040 based on data from the International Energy Agency World Energy Outlook. Kardashev presented for the first time a classification of civilizations according to the level of the rate of their energy consumption, or ability to harness power, in an article entitled Transmission of Information by Extraterrestrial Civilizations, published in 1964 first in ...
Penn alumni are the current or past presidents of over one hundred universities and colleges including Harvard University, University of Pennsylvania, Princeton University, Cornell University, University of California system, University of Texas system, Carnegie Mellon University, Northwestern University, Tulane University, Bowdoin College, and Williams College; and eight medical schools ...
Artificial intelligence (AI), in its broadest sense, is intelligence exhibited by machines, particularly computer systems.It is a field of research in computer science that develops and studies methods and software that enable machines to perceive their environment and use learning and intelligence to take actions that maximize their chances of achieving defined goals. [1]
The Moon is Earth's only natural satellite.It orbits at an average distance of 384,400 km (238,900 mi), about 30 times the diameter of Earth. Tidal forces between Earth and the Moon have synchronized the Moon's orbital period (lunar month) with its rotation period at 29.5 Earth days, causing the same side of the Moon to always face Earth.
This alloy, with the trade-name Galinstan (with the "-stan" referring to the tin, stannum in Latin), has a low melting point of −19 °C (−2.2 °F). [77] It has been suggested that this family of alloys could also be used to cool computer chips in place of water, and is often used as a replacement for thermal paste in high-performance computing.
Studies reported on 26 October 2023 suggest for the first time that Venus may have had plate tectonics during ancient times and, as a result, may have had a more habitable environment, possibly one capable of sustaining life. [24] [25] Venus has gained interest as a case for research into the development of Earth-like planets and their ...